The 64but 12.10 2G live USB was set up on a 32bit 12.04.1 non-UEFI host with 1G persistence.
The USB boots and persistence works on the non-UEFI host.
The USB boots in Secure boot mode but without persistence on a UEFI host.
The /proc/cmdline on the running live media shows the running kernel to be vmlinuz.efi.signed, which of
course does not appear in any syslinux config files.
Looks like something got left out in the secure boot procedure to have persistence.

Live media created with the following iso:
800063488 Mar 18 11:14 ubuntu-12.10-desktop-amd64.iso
md5sum
7ad57cadae955bd04019389d4b9c1dcb ubuntu-12.10-desktop-amd64.iso

The UEFI host is a Toshiba Satellite S855-5378 and has Windows 8 preinstalled,
so no legacy BIOS is present.